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In an era of near constant downsizing, there are at least two conflicting ways to look at raises.

It’s important to be paid what you’re worth.

Pushing for a big raise is pointless. Even if you succeed, being the highest-paid, or among the highest-paid, in your group no longer means you’re performing at a level that will soon earn you a promotion. It means that when the next round of cutbacks come, you might as well have a target on your back.

Now, a new study from four researchers provides some support for the second point of view, using data from a group of extremely well-paid but also extremely sought-after employees-CEOs. The study’s authors, Adam J. Wowak of the University of Notre Dame, Donald C. Hambrick of Pennsylvania State University, and Andrew D. Henderson of the University of Texas at Austin, examined the relationship between CEO pay and performance over a decade. They looked at 590 big company CEOs who had tenures of at least four years between 1996 and 2005. Here’s what they found:

CEOs who are overpaid in their first year become even more overpaid the longer they stay on. As the paper states:

When all other factors are controlled for, CEOs who have been prevailingly overpaid tend to receive the biggest current raises (or smallest pay cuts)… we observed that the rich get richer and the poor get poorer-relatively speaking, of course.

The authors believe that, when it comes to CEO pay, boards get a bit deluded, believing that a CEOs excessive pay is simply a reflection his or her abilities. As long as that CEO is still wearing his or her halo, the board keeps giving him or her big raises, in hopes of keeping the CEO on board and motivated.

CEOs who are overpaid are more likely to be fired. When highly-paid CEOs stumble, they’re especially vulnerable to dismissal. The researchers suggest two explanations for this phenomenon.

The psychological explanation: When a highly-paid CEO stumbles, the board’s response may be almost retaliatory. They’re paying a huge sum of money for a CEO, and suddenly they decide they’re not getting their money’s worth.

The economic explanation: When an overpaid CEO makes a mistake, the board is shocked to realized that no matter how well the CEO performs in the future, he or she is never going to be worth all the money he or she is getting.

The very term “overpaid,” when it comes to CEOs, can admittedly be a little confusing. With average CEO pay up around $12 million, it’s easy to argue that even an “underpaid” CEO makes plenty, and probably more than he or she should. But within the rarefied ranks of CEOs, it does appear that being among the best-paid gives a CEO less leeway to make mistakes.

Does the same phenomenon apply at less-exalted levels of corporate America? Does being among the best-paid of a group of people with the same title–any title–also mean you’re more likely to be fired?